No, the employer is not beside the point. The employer pays your salary. If you do less work, you get less salary. That isn't saying their work isn't valuable, it is saying it isn't valuable to the employer. The person who values work pays for it. In this case, it is the woman herself who values the work. She is literally choosing to pay herself, in the form of a well cared for child. In the same way that when I clean my home, I am choosing to compensate myself for the effort required to do so by having a clean home.
You could have compared it to caring about elderly dad, doing volunteer work or anything else boring, unpaid but useful. Instead, you compared it to playing games which rubs people wrong.
Who cares what the evocation is? Are we not adults capable of following chains of reasoning without descending into literary analogy and euphemism? We're not analyzing Shakespeare here.
and that's the systemic sexism--the systemic choices about what should, and what doesn't need, to be paid for.
why don't we instead have a society where all childcare is paid labor and we just "pay ourselves" for other self-benefitting labor (growing food, for example)?
(collective) assumptions like these are the systemic sexism. note that this is different from calling a specific person a sexist.
> and that's the systemic sexism--the systemic choices about what should, and what doesn't need, to be paid for.
Who is it you think ought to be paying for childcare? It's clear who pays for wage labor. The employer pays for it, because they value it.
> why don't we instead have a society where all childcare is paid labor and we just "pay ourselves" for other self-benefitting labor (growing food, for example)?
The answer to this question is "the entire history of economics and every lesson ever learned about how to structure effective civilizations for the entire history of humanity". I'm not really sure how else to respond to that.